Distribution, assessment, landmarks, digitization,
measurement errors methods and statistical analysis
The species are freely distributed within this geography and rarely
found beyond 7.430 50°N, 8.320 1°E. Images were produced in replicates
and processed in Thin Plate Spline (tps) methods for dorsal and ventral
skull suture digitized landmarks. Measurement errors may arise as a
result of individuals in the population being evaluated and as well as
from replicate residuals in the evaluation; and was accounted for by
taking the landmarks in repeated procedures (replica), measurement error
value contributions were also used in the determination of fluctuating
asymmetry; whereas the former must be insignificant in quantity
contribution when compared to the latter since both are similar in
magnitude and distribution during analysis. Paleontological statistical
software (PAST) version 3.0
(http://folk.uio.no/ohammer/past/) (Hammer et al.,
2001) was employed in all statistical analyses including
homoscedasticity and normality tests in this investigation.
2.4. Symmetric and asymmetric quantities
The components of asymmetry are often quantified with a two-factor
analysis of variance (ANOVA) of individual measurements with the sides
(left and right) and the individuals as the main effects (Leamy 1984;
Palmer and Strobeck 1986), with measurement error when both sides of
each individual are measured repeatedly. Directional asymmetry (DA) is
quantified by the difference between the means of all the configurations
from either body side (left and right) (means of all individual
asymmetries) (Urbanova et al., 2014) and expressed statistically as the
difference in means between the left and right sides in the two-way
ANOVA.